Problem: $A$ $B$ $C$ If: $ AC = 113$, $ BC = 3x + 9$, and $ AB = 8x + 5$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 5} + {3x + 9} = {113}$ Combine like terms: $ 11x + 14 = {113}$ Subtract $14$ from both sides: $ 11x = 99$ Divide both sides by $11$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $BC$ $ BC = 3({9}) + 9$ Simplify: $ {BC = 27 + 9}$ Simplify to find ${BC}$ : $ {BC = 36}$